Ultrasonic sizing of short surface cracks

This paper presents a method for ultrasonic sizing of surface cracks based on time domain and frequency domain Rayleigh wave near-field analysis. The procedure allows for the entire range of ratio of crack depth to Rayleigh wavelength a/λ to be covered with one single measurement. In the time domain the time-of-flight method was extended to cracks smaller than the wavelength by correlation of the time delay of the transmitted Rayleigh wave with the crack depth. In the frequency domain, the inverse scattering problem was solved by comparison of the measured scattering coefficients and central frequencies of the reflected and transmitted Rayleigh waves with theoretical curves. The sizing procedure was demonstrated experimentally with narrow slots and real fatigue cracks. The out-of-plane displacement component was measured pointwise in the scattered near field by means of laser interferometry. The determination of the scattering parameters in the near field was enabled by a procedure that allows for the Rayleigh wave to be separated from the other modes scattered at the defect. The experimental results showed good accuracy and repeatability down to the smallest available ratio of crack depth to Rayleigh wavelength a/λ = 0.15.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

激光激发瑞利波检测表面倾斜缺陷的研究

研究激光激发瑞利波检测样品的表面倾斜缺陷。基于频域热弹耦合方程,采用有限元方法建立激光激发瑞利波检测倾斜缺陷的数值模型,研究倾斜缺陷的检测机理。数值计算含不同的长度及倾斜角度缺陷的样品中瞬态位移波形,分析瑞利波在倾斜缺陷处模式转换的过程,研究各种瑞利波的传播路径。在此基础上,研究缺陷宽度与材料黏性对瑞利波传播及缺陷检测的影响。结果表明:瑞利波在缺陷处产生的反射及透射瑞利波的到达观测点的时间可以检测缺陷位置和长度,瑞利波在缺陷的底部发生模式转换产生的切变波可以检测缺陷倾斜角度。数值结果和已有的实验结果一致,从而为表面倾斜缺陷的检测提供有效的理论依据。      

表面垂直裂痕诱发瑞利波散射的数值分析

激光激发的声表面波为材料表面缺陷的检测提供了有力的工具.针对含缺陷材料在模型边界上的复杂性,建立了基于平面应变的有限元模型并选取了相同厚度但含有不同深度的表面裂痕的单层铝板进行了对比计算,得到了声表面波经过不同深度的表面裂痕时产生的反射及透射信号波形的时域特征.进而引入了基于Wigner-Ville分布理论的时-频分析方法计算裂痕前、后散射的瞬态表面波的能量在时间-频率平面内分布的情形.结果显示：声表面波接近中心频率的某一频率成分在经过深度小于其中心波长的表面缺陷时,随着裂痕深度的增加,对应于该频率的反射系数呈现单调递增的趋势;而透射系数呈现递减的特征,这一结果可以为激光超声检测表面缺陷提供一种定量的表征手段.     

Numerical simulation of Bragg scattering of sound by surface roughness for different values of the Rayleigh parameter

Numerical simulation methods are described for the spectral characteristics of an acoustic signal scattered by multiscale surface waves. The methods include the algorithms for calculating the scattered field by the Kirchhoff method and with the use of an integral equation, as well as the algorithms of surface waves generation with allowance for nonlinear hydrodynamic effects. The paper focuses on studying the spectrum of Bragg scattering caused by surface waves whose frequency exceeds the fundamental low-frequency component of the surface waves by several octaves. The spectrum broadening of the backscattered signal is estimated. The possibility of extending the range of applicability of the computing method developed under small perturbation conditions to cases characterized by a Rayleigh parameter of ≥1 is estimated.     

水下掩埋目标的散射声场计算与实验

水下掩埋目标声散射问题是识别和探测掩埋目标的理论基础, 是声散射研究领域的热点问题. 本文基于射线声学推导了掩埋情况下目标声散射计算的格林函数近似式, 并在此基础上进一步给出了相应的远场积分公式. 在有限元方法的基础上, 将推导得到的公式写入有限元仿真软件, 对软件功能进行拓展, 构建二维轴对称目标的声散射模型, 并计算掩埋情况下弹性实心球在不同条件下的目标强度, 获得了其散射声场随频率、掩埋深度、沙层吸收系数等参数的变化规律. 开展实心球的自由空间和浅掩埋条件下水池声散射实验, 利用共振隔离技术处理实验数据, 提取目标声散射的纯弹性共振特征进行分析, 结果表明可将其用于掩埋目标识别和探测. 最后利用总散射声场与理论计算结果进行对比, 验证了理论仿真的正确性.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

Detection of cracks at rivet holes using guided waves

Guided Lamb waves can be used for a fast inspection of large areas, e.g. the detection of cracks at rivet holes in the fuselage of airplanes. When the guided wave hits a discontinuity like a hole, a typical scattered displacement field is obtained. A change of the scattered field indicates the development of a crack. In the experiments, the first anti-symmetric mode A0 of Lamb waves in plates is excited selectively by means of a piezoelectric transducer. The used frequency range is below the cut-off frequencies of higher wave modes. The scattered field around undamaged and damaged holes is measured on a grid around the hole with a heterodyne laser interferometer. Two types of damage are introduced: a notch cut with a very fine saw blade, and a fatigue grown crack. A significant change in the scattered field due to the defect is seen. Good agreement of the experimental results with theoretical calculations is obtained. The wave propagation is studied using Mindlin's theory of plates. The scattered field is calculated analytically and using finite difference methods (FDMs).     

Analyzing the coda from correlating scattered surface waves

The accuracy of scattered Rayleigh waves estimated using an interferometric method is investigated. Summing the cross correlations of the wave fields measured all around the scatterers yields the Green's function between two excitation points. This accounts for the direct wave and the scattered field (coda). The correlations themselves provide insights into the location of the scatterers, as well as which scatterer is responsible for particular parts of the coda. Furthermore, these measurements confirm a constant-time arrival in the correlations, not part of the Green's function, but which has previously been derived as a result of the generalized optical theorem.     

Effect of the illumination length on the statistical distribution of the field scattered from one-dimensional random rough surfaces: analytical formulae derived from the small perturbation method

We consider a dielectric plane surface with a local cylindrical perturbation illuminated by a monochromatic plane wave. The perturbation is represented by a random function assuming values with a Gaussian probability density with zero mean value. Outside the perturbation zone, the scattered field can be represented by a superposition of a continuous spectrum of outgoing plane waves. The stationary phase method leads to the asymptotic field, the angular dependence of which is given by the scattering amplitudes of the propagating plane waves. The small perturbation method applied to the Rayleigh integral and the boundary conditions gives a first-order approximation of the scattering amplitudes. We show that the real part and the imaginary part of the scattering amplitudes are Gaussian stochastic variables with zero mean values and unequal variances. The values of variances depend on the length of the perturbation zone. In most cases, the probability density function for the amplitude is a Hoyt distribution and the phase is not uniformly distributed between -π and π. The standard Rayleigh and uniform distributions are obtained for special values of the length and in the case of an infinite illumination length.     

Finite element analysis of Rayleigh wave interaction with finite-size,surface-breaking cracks

The interaction of surface acoustic waves with finite-size, surface-breaking, semi-circular cracks is studied numerically, and experimentally. We focus on the behavior of the reflection coefficient of the Rayleigh wave from such cracks in the far field of the crack, when the depth of the crack is comparable to the wavelength of the interrogating surface wave. The cases in which the depth of the crack is much smaller or much larger compared to the wavelength have been extensively investigated by many authors and are not considered here except for validating the numerical and experimental results in these regimes. The theoretical, finite element, and experimental results presented are in very good agreement over the range were the crack depth is much smaller or much larger compared to the wavelength of the incident Rayleigh wave. In the transition regime, between these two limiting cases, only the finite element and experimental data show good agreement since the theoretical predictions are no longer applicable. In the high crack depth to wavelength ratio (a/lambda(R)) regime, the finite element and experimental results close to the crack approach the limiting value of the reflection coefficient from a 90 degrees corner.     

Effect of the illumination length on the statistical distribution of the field scattered from one-dimensional random rough surfaces: analytical formulae derived from the small perturbation method

We consider a dielectric plane surface with a local cylindrical perturbation illuminated by a monochromatic plane wave. The perturbation is represented by a random function assuming values with a Gaussian probability density with zero mean value. Outside the perturbation zone, the scattered field can be represented by a superposition of a continuous spectrum of outgoing plane waves. The stationary phase method leads to the asymptotic field, the angular dependence of which is given by the scattering amplitudes of the propagating plane waves. The small perturbation method applied to the Rayleigh integral and the boundary conditions gives a first-order approximation of the scattering amplitudes. We show that the real part and the imaginary part of the scattering amplitudes are Gaussian stochastic variables with zero mean values and unequal variances. The values of variances depend on the length of the perturbation zone. In most cases, the probability density function for the amplitude is a Hoyt distribution and the phase is not uniformly distributed between –π and π. The standard Rayleigh and uniform distributions are obtained for special values of the length and in the case of an infinite illumination length.     

Reflection of an Ultrashort Pulse by an Ideally Conducting Cylinder

A technique for calculating the backscattering of ultrashort pulses of plane waves by an ideally conducting cylinder is described on the basis of the spectral representation. The Rayleigh solution in the Bessel function series representation is used to determine the scattering spectral components. The Gabor impulse reflection is investigated. A method for remote determination of the cylinder diameter from the shift of scattered field amplitude peaks is described.     

Probing of laser-induced crack modulation by laser-monitored surface waves and surface skimming bulk waves

All-optical monitoring of the nonlinear motion of a surface-breaking crack is reported. Crack closing is induced by quasi-continuous laser heating, while Rayleigh surface acoustic pulses and bulk longitudinal surface skimming acoustic pulses are also generated and detected by lasers. By exploiting the strong dependence of the acoustic pulses reflection and transmission efficiency on the state-open or closed-of the contacts between the crack faces, the parametric modulation of ultrasonic pulses is achieved. It is observed that bulk acoustic waves skimming along the surface can be more sensitive to crack motion than Rayleigh surface waves.     

The far field asymptotics in the problem of diffraction of an acoustic plane wave by an impedance cone

The work deals with the far field asymptotics of the classical solution for the problem of diffraction by an impedance cone. The incident acoustic plane wave completely illuminates the semi-infinite conical surface. The scattered field contains different components in the asymptotics, namely, the spherical wave from the vertex of the cone, the reflected waves, and, under some conditions, also the surface waves of Rayleigh type. We give integral representations for the scattering diagram of the spherical wave. The uniform (with respect to the observation direction) asymptotic expression for the wave field is also addressed and described by the parabolic cylinder ansatz. Dedicated to the memory of Vladimir Borovikov     

Rayleigh's hypothesis and the geometrical optics limit

The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.     

Planar imaging of a laboratory flame and of internal combustion in an automobile engine using UV rayleigh and fluorescence light

Rayleigh scattering of tunable excimer laser light (193 nm and 248 nm) is used to obtain 2-D images of the distribution of total densities in a laboratory flame and in a cylinder of an automobile engine. Because the UV light is very strongly scattered, there is ample signal and there is excellent contrast of Rayleigh light against surface scattered light, even in the small volume of the engine cylinder. The laboratory flame data are converted to an image of the temperature field. The Rayleigh images are compared with those from planar laser induced predissociative fluorescence, which yield state-specific densities of selected molecules. The experimental arrangement is the same except for the selection of laser wavelength and the filtering of the radiated light.     

Analytical derivation of the stationarity and the ergodicity of a field scattered by a slightly rough random surface

In the framework of the small perturbation method, we present a new theoretical derivation of the statistical and spatial properties of a field scattered by a one-dimensional slightly rough random surface. The work concerns the intermediate field zone where the scattered field is reduced to the contribution of the progressive plane waves. The surface is assumed to be stationary, ergodic and Gaussian. First, from a statistical point of view, we demonstrate that under oblique incidence the scattered field is not stationary while it is strictly stationary under normal incidence. For an infinite surface, the scattered field modulus obeys to Hoyt law and the phase is not uniform. Second, from a spatial point of view, for a given altitude and under all incidences, we show that the scattered field is ergodic. Under oblique incidence, the phase is spatially uniform and the modulus is given by a Rayleigh law. Under normal incidence, the phase is not uniform and the modulus is given by a Hoyt law. Third, from a practical point of view, we show that the field measured by a directional antenna is ergodic and stationary if the angular transfer function of the antenna does not contain the specular direction.     

Frequency-wavenumber domain analysis of guided wavefields

Full wavefield measurements obtained with either an air-coupled transducer mounted on a scanning stage or a scanning laser vibrometer can be combined with effective signal and imaging processing algorithms to support characterization of guided waves as well as detection, localization and quantification of structural damage. These wavefield images contain a wealth of information that clearly shows details of guided waves as they propagate outward from the source, reflect from specimen boundaries, and scatter from discontinuities within the structure. The analysis of weaker scattered waves is facilitated by the removal of source waves and the separation of wave modes, which is effectively achieved via frequency-wavenumber domain filtering in conjunction with the subsequent analysis of the resulting residual signals. Incident wave removal highlights the presence and the location of weak scatterers, while the separation of individual guided wave modes allows the characterization of their separate contribution to the scattered field and the evaluation of mode conversion phenomena. The effectiveness of these methods is demonstrated through their application to detection of a delamination in a composite plate and detection of a crack emanating from a hole.     

Noncolinear Second-Harmonic Generation Pairs and Their Scatterings in Nd~(3+):SBN Crystals with Needle-Like Ferroelectric Domains

Second-harmonic generation in Nd~(3+):SBN crystal with needle-like ferroelectric with aperiodic domain structures is investigated. Two pairs of second harmonic(SH) waves appearing in lines are observed in unpoled Nd~(3+):SBN crystals with aperiodic needle-like domains. A pair of SH waves emit from the exit face, whose intensities are angle-dependent. The angular dependence is corresponding to the spatial frequency spectrum of the aperiodic domain structure. Another pair of SH waves emit from both the side surfaces, which are mainly the scattered SH waves by needle-like domain walls and obey the theory of Rayleigh scattering.